Find the cmf of the terms    7a² +15a   6x²+12  24m²-16m   2b-4c  8u+36v

To find the **common monomial factor (CMF)** of the given terms, we identify the greatest common factor (GCF) of the coefficients and the common variables with the lowest power in each expression.

Here are the terms:
1. \( 7a^2 + 15a \)
2. \( 6x^2 + 12 \)
3. \( 24m^2 - 16m \)
4. \( 2b - 4c \)
5. \( 8u + 36v \)

### Step-by-Step Analysis:

1. **\( 7a^2 + 15a \):**
   - Coefficients: 7 and 15
   - GCF of coefficients: 1 (since 7 and 15 have no common factor other than 1)
   - Variables: \( a^2 \) and \( a \)
   - Common variable: \( a \)

   CMF for this term: \( a \)

2. **\( 6x^2 + 12 \):**
   - Coefficients: 6 and 12
   - GCF of coefficients: 6
   - Variables: \( x^2 \) and constant (no variable)

   CMF for this term: \( 6 \)

3. **\( 24m^2 - 16m \):**
   - Coefficients: 24 and 16
   - GCF of coefficients: 8
   - Variables: \( m^2 \) and \( m \)
   - Common variable: \( m \)

   CMF for this term: \( 8m \)

4. **\( 2b - 4c \):**
   - Coefficients: 2 and 4
   - GCF of coefficients: 2
   - Variables: \( b \) and \( c \) (no common variable)

   CMF for this term: \( 2 \)

5. **\( 8u + 36v \):**
   - Coefficients: 8 and 36
   - GCF of coefficients: 4
   - Variables: \( u \) and \( v \) (no common variable)

   CMF for this term: \( 4 \)

### Common Monomial Factor (CMF):

The **common monomial factor** for all the given terms is **1** since there is no common factor that can be factored out from each expression.

Do you want details or have any questions? Here are five questions for further exploration:

1. How do you factor out the greatest common factor (GCF) from a polynomial?
2. What is the significance of finding the CMF in algebraic expressions?
3. How do you handle variables when determining the CMF?
4. Can you apply the concept of CMF to expressions with more complex variables?
5. What are some real-world applications of factoring polynomials?

**Tip:** Always start by finding the greatest common factor of the coefficients before considering the variables.

Learn how to find the common monomial factor (CMF) of polynomials step-by-step with detailed explanations. This problem involves identifying the greatest common factor (GCF) of coefficients and variables in algebraic expressions. Suitable for Grades 7-9.

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